CN113270903A - Load recovery double-layer optimization method considering time-varying step length - Google Patents

Load recovery double-layer optimization method considering time-varying step length Download PDF

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CN113270903A
CN113270903A CN202110710597.9A CN202110710597A CN113270903A CN 113270903 A CN113270903 A CN 113270903A CN 202110710597 A CN202110710597 A CN 202110710597A CN 113270903 A CN113270903 A CN 113270903A
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load
node
formula
time step
recovery
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CN113270903B (en
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孙磊
杨智超
李明明
丁明
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Hefei University of Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/48—Controlling the sharing of the in-phase component
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/12—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load
    • H02J3/14—Circuit arrangements for ac mains or ac distribution networks for adjusting voltage in ac networks by changing a characteristic of the network load by switching loads on to, or off from, network, e.g. progressively balanced loading
    • H02J3/144—Demand-response operation of the power transmission or distribution network
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/46—Controlling of the sharing of output between the generators, converters, or transformers
    • H02J3/50—Controlling the sharing of the out-of-phase component
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/30—Systems integrating technologies related to power network operation and communication or information technologies for improving the carbon footprint of the management of residential or tertiary loads, i.e. smart grids as climate change mitigation technology in the buildings sector, including also the last stages of power distribution and the control, monitoring or operating management systems at local level
    • Y02B70/3225—Demand response systems, e.g. load shedding, peak shaving
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S20/00—Management or operation of end-user stationary applications or the last stages of power distribution; Controlling, monitoring or operating thereof
    • Y04S20/20—End-user application control systems
    • Y04S20/222—Demand response systems, e.g. load shedding, peak shaving

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Abstract

The invention discloses a load recovery double-layer optimization method considering time-varying step length, which comprises the following steps: considering direct current power flow constraint, cold load characteristic constraint and the like, establishing a load recovery upper-layer optimization model by taking the maximum weighted load recovery quantity as an optimization target; because the upper layer model does not consider network loss and reactive power output and the direct current power flow calculation has errors, the alternating current power flow constraint, the node voltage safety constraint and the like are considered, and the load recovery lower layer optimization model is established by taking the current time step shortest load recovery step length as an optimization target; modeling is carried out on AMPL optimization software, solvers CPLEX and SNOPT are called to carry out iterative solution, and the optimal load recovery scheme under the current time-step shortest load recovery step length is obtained. The method can effectively obtain the optimal load recovery scheme and the shortest load recovery duration time in different power system running states, thereby improving the speed of actual power system load recovery and shortening the power failure time of the power system.

Description

Load recovery double-layer optimization method considering time-varying step length
Technical Field
The invention relates to the field of power system recovery, in particular to a double-layer optimization method under consideration of grid-load cooperative recovery optimization in load recovery.
Background
Load recovery is a multi-time-step process, most researches adopt fixed time to model the load recovery process, and the main defect is that the uncertainty of parameters can influence the optimization result of the fixed time and even lead to the reformulation of a recovery scheme. In the initial stage of load recovery, although the main grid frame of the power system is recovered, a part of lines are not recovered, and a load recovery scheme which is made by ignoring the unrecovered lines may fail in the implementation process, so that the recovery time is prolonged, and even a power failure is caused again. In addition, the cold load effect during load recovery increases the risk of safe and stable operation of the power system. Therefore, how to comprehensively solve the single-time-step load recovery optimization problem and the cold load modeling problem in the network-load cooperative recovery optimization process needs to be further explored.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a load recovery double-layer optimization method considering time-varying step length, so that the influence of cold load characteristics in the recovery process can be considered, and the optimal load recovery scheme under the shortest load recovery duration is obtained aiming at different running states in the recovery process of the power system, so that the load recovery speed of the actual power system is increased, and the power failure time of the power system is shortened.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the invention relates to a load recovery double-layer optimization method considering time-varying step length, which is characterized by being applied to a load recovery stage of a power system, wherein the power system comprises a wind storage combined system, load nodes considering cold load characteristics, unit nodes and power transmission lines among the nodes, a linearized cold load characteristic curve is established according to the load capacity of each load node, and the load recovery double-layer optimization method is carried out according to the following steps:
step one, establishing a load recovery upper-layer optimization model based on direct current power flow:
step 1.1, defining an objective function for maximizing the weighted load amount at the kth time step by using the formula (1):
Figure BDA0003133566290000011
in formula (1): omegaBIs a set of all nodes in the power system;
Figure BDA0003133566290000012
a set of load points to be recovered on the ith load node at the kth time step; w is ai,hThe weight of the h load point on the ith load node is obtained;
Figure BDA0003133566290000013
the active load demand of the h load point on the ith load node is obtained; c. Ci,h,kThe cold load coefficient of the h load point on the ith load node at the kth time step; z is a radical ofi,h,kIs the recovery state of the h load point on the ith load node at the k time step, if z isi,h,k1, denotes the h-th load point recovery, if z i,h,k0; indicating that the h load point is not restored;
step 1.2, establishing direct current power flow constraint by using the formula (2) to the formula (7):
Figure BDA0003133566290000021
Figure BDA0003133566290000022
Figure BDA0003133566290000023
Figure BDA0003133566290000024
Figure BDA0003133566290000025
Figure BDA0003133566290000026
formula (2) to formula (7):
Figure BDA0003133566290000027
the maximum power angle difference of the power transmission line between the ith node and the jth node is represented; sij,kThe recovery state of the power transmission line between the ith node and the jth node at the kth time step is shown, if s ij,k1, the power transmission line between the ith node and the jth node is recovered at the kth time step, if sij,kWhen the transmission line is not recovered, the transmission line between the ith node and the jth node is not recovered; deltai,kThe phase angle of the ith node in the kth time step; x is the number ofijRepresenting the reactance of the transmission line between the ith node and the jth node;
Figure BDA0003133566290000028
the active power transmitted on the transmission line between the ith node and the jth node at the kth time step;
Figure BDA0003133566290000029
the set of the transmission lines to be recovered at the kth time step;
Figure BDA00031335662900000210
the set of the recovered transmission lines at the k-1 time step;
Figure BDA00031335662900000211
the maximum active power which can be transmitted on the power transmission line between the ith node and the jth node is obtained;
Figure BDA00031335662900000212
active power output scheduled by the wind storage combined system on the ith node at the kth time step;
Figure BDA00031335662900000213
the active power output by the ith unit node at the kth time step; omegaLRepresenting a set of transmission lines;
Figure BDA00031335662900000214
the active load demand on the ith load node at the kth time step;
Figure BDA00031335662900000215
is the maximum phase angle at the ith node;
step 1.3, establishing a cold load constraint by using an equation (8) to an equation (14):
Figure BDA00031335662900000216
Figure BDA00031335662900000217
Figure BDA00031335662900000218
Figure BDA00031335662900000219
Figure BDA00031335662900000220
Figure BDA00031335662900000221
Figure BDA00031335662900000222
formula (8) -formula (14):
Figure BDA00031335662900000223
considering the active load demand after the cold load characteristic for the h load point on the ith load node at the kth time step;
Figure BDA00031335662900000224
the maximum active load after the cold load characteristic is considered for the h load point on the ith load node; lambda [ alpha ]i,h,αThe slope of a linear cold load characteristic curve of an h load point on an ith load node in an alpha section; zetai,h,α,kIs an auxiliary variable and represents the recovery time of the h load point on the i load node at the k time step in the interval
Figure BDA0003133566290000031
The length of time of the inner;
Figure BDA0003133566290000032
an alpha segment point of the linearized cooling load characteristic curve representing the h load point on the i load node;
Figure BDA0003133566290000033
an alpha-1 segment point of a linearized cooling load characteristic curve representing an h load point on an i load node;
Figure BDA0003133566290000034
representing the set of restored load points at time step k-1; t is ti,h,k-1The time that the h load point on the ith load node is recovered at the k-1 time step is represented; Δ tk,scRepresenting the load recovery duration of the load recovery upper-layer optimization model at the kth time step; n represents the number of segmentation points of the linearized cold load characteristic curve; v. ofi,h,α,kIs a Boolean variable and indicates whether the recovery time length of the h load point on the i load node at the k time step is linearIn the alpha section of the cooling load characteristic curve;
step 1.4, establishing unit output constraint by using the formula (15) to the formula (17):
Figure BDA0003133566290000035
Figure BDA0003133566290000036
Figure BDA0003133566290000037
formula (15) to formula (17):
Figure BDA0003133566290000038
representing the maximum active power allowed to be output by the g-th unit node at the k-th time step;
Figure BDA0003133566290000039
the active power output by the g unit node at the k-1 time step; r isgThe grade climbing rate of the g-th unit node is obtained;
Figure BDA00031335662900000310
the maximum active power allowed to be output for the g-th unit node; omegaGThe method comprises the steps of (1) collecting unit nodes;
Figure BDA00031335662900000311
representing the minimum active power allowed to be output by the g-th unit node at the k-th time step;
Figure BDA00031335662900000312
the minimum active power allowed to be output for the g-th unit node;
Figure BDA00031335662900000313
the active power actually output by the g-th unit node at the k-th time step;
step 1.5, establishing an optimal load input amount constraint by using an equation (18):
Figure BDA00031335662900000314
in formula (18):
Figure BDA00031335662900000315
the maximum load input allowed by the power system at the kth time step;
step 1.6, establishing unit standby constraint by using the formula (19) to the formula (20):
Figure BDA00031335662900000316
Figure BDA00031335662900000317
formula (19) -formula (20):
Figure BDA00031335662900000318
the reserve capacity of the g unit node at the k time step; rhogRepresenting the ratio of the reserve capacity of the g-th unit node in the total active output of the unit node;
step 1.7, establishing recovery state constraint by using the formula (21) to the formula (24):
Figure BDA00031335662900000319
Figure BDA00031335662900000320
Figure BDA0003133566290000041
Figure BDA0003133566290000042
formula (20) to formula (24): y isi,kIndicating the recovery state of the ith node at the kth time step if y i,k1, indicates that the ith node has recovered, if y i,k0, which means that the ith node is not recovered; ε is a constant;
Figure BDA0003133566290000043
the maximum load point number on the ith node is obtained;
step 1.8, establishing wind storage combined system dispatching output constraint by using a formula (25):
Figure BDA0003133566290000044
in formula (25):
Figure BDA0003133566290000045
the minimum active power output of the wind storage combined system accessed by the ith node at the kth time step;
Figure BDA0003133566290000046
the dispatching output of the wind storage combined system accessed by the ith node at the kth time step is obtained;
Figure BDA0003133566290000047
the maximum active power output of the wind storage combined system accessed by the ith node at the kth time step; omegaB,WThe method comprises the steps of collecting nodes of an accessed wind storage combined system;
step 1.9, the objective function shown in the formula (1) and the constraint conditions shown in the formulas (2) to (25) jointly form the load recovery upper-layer optimization model;
step two, establishing a load recovery lower-layer optimization model based on the alternating current power flow:
step 2.1, defining an objective function that minimizes the load recovery duration of the kth time step using equation (26):
minΔtk,xc (26)
in formula (26): Δ tk,xcLoad recovery duration for the load recovery underlying optimization model;
step 2.2, establishing an alternating current power flow constraint by using the formula (27) to the formula (28):
Figure BDA0003133566290000048
Figure BDA0003133566290000049
formula (27) to formula (28): u shapei,kThe voltage value of the ith node at the kth time step is shown;
Figure BDA00031335662900000410
restoring the power transmission line set restored by the upper-layer optimization model for the load at the kth time step; gijThe conductance value of the power transmission line between the ith node and the jth node is obtained; b isijThe susceptance value of the power transmission line between the ith node and the jth node is obtained;
Figure BDA00031335662900000411
the reactive power output of the ith unit node at the kth time step;
Figure BDA00031335662900000412
the reactive load demand on the ith load node at the kth time step;
and 2.3, jointly forming a load constraint considering the cold load characteristic in the load recovery lower-layer optimization model by using the formula (8), the formula (10) -the formula (13) and the formula (29) -the formula (31):
Figure BDA00031335662900000413
Figure BDA00031335662900000414
Figure BDA00031335662900000415
formula (29) -formula (31):
Figure BDA0003133566290000051
restoring the node set restored by the upper-layer optimization model for the load at the kth time step; omegai DA set of load points on the ith load node;
step 2.4, establishing a unit output constraint by using the formula (32) -the formula (36):
Figure BDA0003133566290000052
Figure BDA0003133566290000053
Figure BDA0003133566290000054
Figure BDA0003133566290000055
Figure BDA0003133566290000056
formula (32) -formula (36):
Figure BDA0003133566290000057
representing the minimum reactive power allowed to be output by the g unit node;
Figure BDA0003133566290000058
for the g-th group node at the k-th time stepThe output reactive power;
Figure BDA0003133566290000059
representing the maximum reactive power allowed to be output by the g-th unit node;
step 2.5, establishing node voltage constraint by using the formula (37):
Figure BDA00031335662900000510
and 2.6, establishing a current step size correlation constraint by using an equation (38):
-Δtmin≤Δtk,xc-Δtk,sc≤Δtmin (38)
in the formula: Δ tminThe minimum difference of the recovery duration between the load recovery upper-layer optimization model and the load recovery lower-layer optimization model is obtained;
step 2.7, the objective function shown in the formula (26) and the formula (8), the formula (10) -the formula (13), the formula (19), the formula (20), the formula (25) and the formula (27) -the formula (38) jointly form the load recovery lower layer optimization model;
step three, solving a load recovery double-layer optimization model considering the time-varying step length:
step 3.1, inputting initial data of the power system in the load recovery stage, wherein the initial data comprises the following steps: the output of the unit node, the load quantity of the recovered/unrecovered load point and the initial running state of the power system; and initializing k to 1;
step 3.2, solving a load recovery double-layer optimization model considering the step length of the time-varying step under the kth time step;
step 3.2.1, solving the load recovery upper layer optimization model by utilizing a solver CPLEX to obtain an optimal load recovery result at the kth time step, wherein the method comprises the following steps: the load point is recovered, and the transmission line is recovered;
step 3.2.2, transmitting the optimal load recovery scheme to the load recovery lower-layer optimization model, and solving the load recovery lower-layer optimization model by using a nonlinear solver SNOPT to obtain the shortest load recovery duration and the output of the optimal unit at the kth time step;
step 3.2.3, judging whether the load recovery double-layer optimization model at the kth time step meets the iteration termination condition, if so, executing the step 3.3, otherwise, after transmitting the optimal load recovery duration at the kth time step to the load recovery upper-layer optimization model, returning to the step 3.2.1; wherein the iteration termination condition is | Δ tk,sc-Δtk,xcDelta is less than or equal to | and the load recovery amount under the current time step is not changed any more;
step 3.3, outputting the optimal load recovery scheme of the kth time step, comprising: recovering the load point, the power transmission line, the duration and the output of the optimal unit;
and 3.4, judging whether all load points of the power system are recovered at the kth time step, if so, outputting an optimal load recovery scheme from the 1 st time step to the kth time step, otherwise, updating the running state of the power system, and returning to the step 3.2 after k +1 is assigned with k.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention considers the optimal load recovery schemes under different running states in the recovery process of the power system, provides a load recovery optimization model based on single time step, solves the problem that the power failure time of the power system is prolonged by adopting fixed time step length in the formulation process of the load recovery scheme of the power system, and improves the recovery speed of the power system.
2. The invention provides a load recovery double-layer optimization framework, which effectively reduces the calculated amount, avoids the multi-objective optimization problem, reduces the difficulty of making a load recovery scheme of an electric power system and provides a new research idea for the load recovery problem of the electric power system.
3. The invention provides the linear constraint of the cold load characteristics, is suitable for a load recovery optimization method considering time-varying step length, solves the problem that the cold load constraint considering the time-varying characteristics is difficult to apply to the time-varying step optimization problem, and improves the accuracy of the actual load recovery scheme of the power system.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a flow chart of the method of the present invention.
Detailed Description
In this embodiment, as shown in fig. 1, a load recovery double-layer optimization method considering a time-varying step length is applied to a load recovery stage of an electric power system, where the electric power system includes a wind power storage combined system, load nodes considering a cold load characteristic, a unit node, and an electric transmission line between the nodes, and a linearized cold load characteristic curve is established according to a load amount of each load node, and the method includes the main steps of: considering direct current power flow constraint, cold load characteristic constraint and the like, establishing a load recovery upper-layer optimization model by taking the maximum weighted load recovery quantity as an optimization target; because the upper layer model does not consider network loss and reactive power output and the direct current power flow calculation has errors, the alternating current power flow constraint, the node voltage safety constraint and the like are considered, and the load recovery lower layer optimization model is established by taking the current time step shortest load recovery step length as an optimization target; modeling is carried out on AMPL optimization software, solvers CPLEX, SNOPT/MINOS are called to carry out iterative solution, and the optimal load recovery scheme under the current time-step shortest load recovery step length is obtained. Specifically, the method comprises the following steps:
step one, establishing a load recovery upper-layer optimization model based on direct current power flow:
step 1.1, defining an objective function for maximizing the weighted load amount at the kth time step by using the formula (1):
Figure BDA0003133566290000071
in formula (1): omegaBIs a set of all nodes in the power system;
Figure BDA0003133566290000072
a set of load points to be recovered on the ith load node at the kth time step; w is ai,hFor the ith load nodeWeight of the h-th load point on the point;
Figure BDA0003133566290000073
the active load demand of the h load point on the ith load node is obtained; c. Ci,h,kThe cold load coefficient of the h load point on the ith load node at the kth time step; z is a radical ofi,h,kIs the recovery state of the h load point on the ith load node at the k time step, if z isi,h,k1, denotes the h-th load point recovery, if z i,h,k0; indicating that the h load point is not restored;
step 1.2, establishing direct current power flow constraint by using the formula (2) to the formula (7):
Figure BDA0003133566290000074
Figure BDA0003133566290000075
Figure BDA0003133566290000076
Figure BDA0003133566290000077
Figure BDA0003133566290000078
Figure BDA0003133566290000079
the formula (2) and the formula (3) respectively represent direct current flow expressions of the kth time step to-be-recovered power transmission line and the kth-1 time step recovered power transmission line; the formula (4) and the formula (5) respectively represent the maximum/minimum power flow constraint of the power transmission line to be recovered at the kth time step and the recovered power transmission line at the kth-1 time step; equation (6) represents a node balance equation; equation (7) represents the maximum/minimum phase angle constraint for the node;
formula (2) to formula (7):
Figure BDA00031335662900000710
the maximum power angle difference of the power transmission line between the ith node and the jth node is represented; sij,kThe recovery state of the power transmission line between the ith node and the jth node at the kth time step is shown, if sij,k1, the power transmission line between the ith node and the jth node is recovered at the kth time step, if sij,kWhen the transmission line is not recovered, the transmission line between the ith node and the jth node is not recovered; deltai,kThe phase angle of the ith node in the kth time step; x is the number ofijRepresenting the reactance of the transmission line between the ith node and the jth node;
Figure BDA00031335662900000711
the active power transmitted on the transmission line between the ith node and the jth node at the kth time step;
Figure BDA00031335662900000712
the set of the transmission lines to be recovered at the kth time step;
Figure BDA00031335662900000713
the set of the recovered transmission lines at the k-1 time step;
Figure BDA00031335662900000714
the maximum active power which can be transmitted on the power transmission line between the ith node and the jth node is obtained;
Figure BDA00031335662900000715
active power output scheduled by the wind storage combined system on the ith node at the kth time step;
Figure BDA00031335662900000716
the active power output by the ith unit node at the kth time step; omegaLRepresenting a set of transmission lines;
Figure BDA00031335662900000717
the active load demand on the ith load node at the kth time step;
Figure BDA00031335662900000718
is the maximum phase angle at the ith node;
step 1.3, establishing a cold load constraint by using an equation (8) to an equation (14):
Figure BDA00031335662900000719
Figure BDA0003133566290000081
Figure BDA0003133566290000082
Figure BDA0003133566290000083
Figure BDA0003133566290000084
Figure BDA0003133566290000085
Figure BDA0003133566290000086
equation (8) represents that the active load demand considering the cold load characteristic is equal to the maximum active load capacity minus the load decay amount; the expression (9) shows that the sum of the recovered time of the load point h on the kth-1 time step node i and the load recovery time of the kth time step is equal to the load recovery ending time of the kth time step, and the value is the sum of the auxiliary variables; expression (10) to expression (13) indicate that the recovery time of the load point h on the node i is within a certain period of the cold load curve; equation (14) represents that the active load demand of the kth time step node i is equal to the amount of the recovered load point of the kth time step-1 plus the active load demand of the kth time step optimized recovery multiplied by the cold load coefficient;
formula (8) -formula (14):
Figure BDA0003133566290000087
considering the active load demand after the cold load characteristic for the h load point on the ith load node at the kth time step;
Figure BDA0003133566290000088
the maximum active load after the cold load characteristic is considered for the h load point on the ith load node; lambda [ alpha ]i,h,αThe slope of a linear cold load characteristic curve of an h load point on an ith load node in an alpha section; zetai,h,α,kIs an auxiliary variable and represents the recovery time of the h load point on the i load node at the k time step in the interval
Figure BDA0003133566290000089
The length of time of the inner;
Figure BDA00031335662900000810
an alpha segment point of the linearized cooling load characteristic curve representing the h load point on the i load node;
Figure BDA00031335662900000811
an alpha-1 segment point of a linearized cooling load characteristic curve representing an h load point on an i load node;
Figure BDA00031335662900000812
representing the set of restored load points at time step k-1; t is ti,h,k-1The time that the h load point on the ith load node is recovered at the k-1 time step is represented; Δ tk,scRepresenting the load recovery duration of the load recovery upper-layer optimization model at the kth time step; n represents a linearized cooling load characteristic curveThe number of segmentation points of the line; v. ofi,h,α,kThe recovery time length of the h load point on the i load node at the k time step is represented by a Boolean variable, and whether the recovery time length is in the alpha section of the linear cooling load characteristic curve or not is represented;
step 1.4, establishing unit output constraint by using the formula (15) to the formula (17):
Figure BDA00031335662900000813
Figure BDA00031335662900000814
Figure BDA00031335662900000815
the formula (15) and the formula (16) are used for calculating the maximum/minimum active output of the kth time-stepping unit g; the formula (17) is used for constraining the active output of the kth time step unit g to be within the range of the maximum/minimum threshold value of the kth time step unit g;
formula (15) to formula (17):
Figure BDA0003133566290000091
representing the maximum active power allowed to be output by the g-th unit node at the k-th time step;
Figure BDA0003133566290000092
the active power output by the g unit node at the k-1 time step; r isgThe grade climbing rate of the g-th unit node is obtained;
Figure BDA0003133566290000093
the maximum active power allowed to be output for the g-th unit node; omegaGThe method comprises the steps of (1) collecting unit nodes;
Figure BDA0003133566290000094
representing the minimum active power allowed to be output by the g-th unit node at the k-th time step;
Figure BDA0003133566290000095
the minimum active power allowed to be output for the g-th unit node;
Figure BDA0003133566290000096
the active power actually output by the g-th unit node at the k-th time step;
step 1.5, establishing an optimal load input amount constraint by using an equation (18):
Figure BDA0003133566290000097
in formula (18):
Figure BDA0003133566290000098
the maximum load input allowed by the power system at the kth time step; the expression (18) shows that the sum of the recovered load amount of the k time step does not exceed the maximum load input amount allowed by the system, and is used for limiting the stability of the frequency in the recovery process;
step 1.6, establishing unit standby constraint by using the formula (19) to the formula (20):
Figure BDA0003133566290000099
Figure BDA00031335662900000910
formula (19) shows that the sum of the active output and the reserve capacity of the kth time-step unit g does not exceed the maximum active output of the current time-step unit; the formula (20) is used for restricting the reserve capacity of the kth time step unit g;
formula (19) -formula (20):
Figure BDA00031335662900000911
the reserve capacity of the g unit node at the k time step; rhogRepresenting the ratio of the reserve capacity of the g-th unit node in the total active output of the unit node;
step 1.7, establishing recovery state constraint by using the formula (21) to the formula (22):
Figure BDA00031335662900000912
Figure BDA00031335662900000913
Figure BDA00031335662900000914
Figure BDA00031335662900000915
formula (20) -formula (23) indicate that the necessary condition for recovering the node i in the kth time step is that at least one power transmission line connected with the node i is recovered or at least one load point on the node i is recovered; equation (24) represents recovering only one transmission line per time step;
formula (21) to formula (24): y isi,kIndicating the recovery state of the ith node at the kth time step if y i,k1, indicates that the ith node has recovered, if y i,k0, which means that the ith node is not recovered; ε is a constant;
Figure BDA00031335662900000916
the maximum load point number on the ith node is obtained;
step 1.8, establishing wind storage combined system dispatching output constraint by using a formula (25):
Figure BDA00031335662900000917
in formula (25):
Figure BDA00031335662900000918
is the ith node place at the kth time stepThe minimum active power output of the accessed wind storage combined system;
Figure BDA00031335662900000919
the dispatching output of the wind storage combined system accessed by the ith node at the kth time step is obtained;
Figure BDA0003133566290000101
the maximum active power output of the wind storage combined system accessed by the ith node at the kth time step; omegaB,WThe method comprises the steps of collecting nodes of an accessed wind storage combined system;
step 1.9, the target function shown in the formula (1) and the constraint conditions shown in the formulas (2) to (25) jointly form the load recovery upper-layer optimization model, and the optimal load recovery scheme under the current step length can be obtained by solving by adopting the fixed time step length;
step two, establishing a load recovery lower-layer optimization model based on the alternating current power flow:
step 2.1, defining an objective function that minimizes the load recovery duration of the kth time step using equation (26):
minΔtk,xc (26)
in formula (26): Δ tk,xcLoad recovery duration for the load recovery underlying optimization model;
step 2.2, establishing an alternating current power flow constraint by using the formula (27) to the formula (28):
Figure BDA0003133566290000102
Figure BDA0003133566290000103
equations (27) and (28) represent an alternating current power flow expression of the kth time step node i, wherein equation (27) takes the kth time step wind storage combined system scheduling output into consideration;
formula (27) to formula (28): u shapei,kThe voltage value of the ith node at the kth time step is shown;
Figure BDA0003133566290000104
restoring the power transmission line set restored by the upper-layer optimization model for the load at the kth time step; gijThe conductance value of the power transmission line between the ith node and the jth node is obtained; b isijThe susceptance value of the power transmission line between the ith node and the jth node is obtained;
Figure BDA0003133566290000105
the reactive power output of the ith unit node at the kth time step;
Figure BDA0003133566290000106
the reactive load demand on the ith load node at the kth time step;
and 2.3, jointly forming a load constraint considering the cold load characteristic in the load recovery lower-layer optimization model by using the formula (8), the formula (10) -the formula (13) and the formula (29) -the formula (31):
Figure BDA0003133566290000107
Figure BDA0003133566290000108
Figure BDA0003133566290000109
equation (29) shows that the load amount recovered by the load point h at the kth time step node i is equal to the maximum active load amount thereof due to the cold load characteristic; the formula (30) has the same meaning as the formula (9) except that the load recovery duration in the formula (30) is a variable; equation (31) represents that the active load demand of the node i is equal to the active load demand of all load points on the node i;
formula (29) -formula (31):
Figure BDA00031335662900001010
restoring nodes of the upper-layer optimization model for the load at the kth time stepGathering; omegai DA set of load points on the ith load node;
step 2.4, establishing a unit output constraint by using the formula (32) -the formula (36):
Figure BDA0003133566290000111
Figure BDA0003133566290000112
Figure BDA0003133566290000113
Figure BDA0003133566290000114
Figure BDA0003133566290000115
since the unit output and the load recovery duration in the load recovery underlying model are both variable, it is necessary to perform linearization processing on equations (15) and (16). The equations (32) and (33) are used for constraining the minimum active output of the kth time step unit g; equations (34) and (35) are used for constraining the maximum active output of the kth time step unit g; equation (36) is used to constrain the reactive power output of the kth time step group g within its maximum/minimum threshold range;
formula (32) -formula (36):
Figure BDA0003133566290000116
representing the minimum reactive power allowed to be output by the g unit node;
Figure BDA0003133566290000117
the real output reactive power of the g-th unit node in the k-th time step;
Figure BDA0003133566290000118
representing the maximum reactive power allowed to be output by the g-th unit node;
step 2.5, establishing node voltage constraint by using the formula (37):
Figure BDA0003133566290000119
equation (37) indicates that if node i recovers at the kth time step, the voltage should be within its threshold range, otherwise the voltage at node i is 0; and 2.6, establishing a current step size correlation constraint by using an equation (38):
-Δtmin≤Δtk,xc-Δtk,sc≤Δtmin (38)
in formula (38): Δ tminThe minimum difference of the recovery duration between the load recovery upper-layer optimization model and the load recovery lower-layer optimization model is obtained; the formula (38) is used for restricting the step length of the upper/lower layer model load recovery time step not to exceed the acceptable range;
step 2.7, the load recovery lower-layer optimization model is formed by the objective function shown in the formula (26) and the formula (8), the formula (10) -the formula (13), the formula (19), the formula (20), the formula (25) and the formula (27) -the formula (38), and the optimal load recovery duration under the current load recovery scheme is solved and obtained on the basis of the optimal load recovery scheme solved by the load recovery upper-layer optimization model;
step three, solving the load recovery double-layer optimization model considering the time-varying step length, wherein the solving process is shown in figure 2:
step 3.1, inputting initial data of the power system in the load recovery stage, wherein the initial data comprises the following steps: the output of the unit node, the load quantity of the recovered/unrecovered load point and the initial running state of the power system; and initializing k to 1;
step 3.2, solving a load recovery double-layer optimization model considering the step length of the time-varying step under the kth time step;
step 3.2.1, solving the load recovery upper layer optimization model by utilizing a solver CPLEX to obtain an optimal load recovery result at the kth time step, wherein the method comprises the following steps: the load point is recovered, and the transmission line is recovered;
step 3.2.2, transmitting the optimal load recovery scheme to the load recovery lower-layer optimization model, and solving the load recovery lower-layer optimization model by using a nonlinear solver SNOPT to obtain the shortest load recovery duration and the output of the optimal unit at the kth time step;
step 3.2.3, judging whether the load recovery double-layer optimization model at the kth time step meets the iteration termination condition, if so, executing the step 3.3, otherwise, after transmitting the optimal load recovery duration at the kth time step to the load recovery upper-layer optimization model, returning to the step 3.2.1; wherein the iteration termination condition is | Δ tk,sc-Δtk,xcDelta is less than or equal to | and the load recovery amount under the current time step is not changed any more;
step 3.3, outputting the optimal load recovery scheme of the kth time step, comprising: recovering the load point, the power transmission line, the duration and the output of the optimal unit;
and 3.4, judging whether all load points of the power system are recovered at the kth time step, if so, outputting an optimal load recovery scheme from the 1 st time step to the kth time step, otherwise, updating the running state of the power system, and returning to the step 3.2 after k +1 is assigned with k.

Claims (1)

1. A load recovery double-layer optimization method considering time-varying step length is characterized by being applied to a load recovery stage of a power system, wherein the power system comprises a wind storage combined system, load nodes considering cold load characteristics, unit nodes and power transmission lines among the nodes, a linear cold load characteristic curve is established according to the load capacity of each load node, and the load recovery double-layer optimization method is carried out according to the following steps:
step one, establishing a load recovery upper-layer optimization model based on direct current power flow:
step 1.1, defining an objective function for maximizing the weighted load amount at the kth time step by using the formula (1):
Figure FDA0003133566280000011
in formula (1): omegaBIs a set of all nodes in the power system;
Figure FDA0003133566280000012
a set of load points to be recovered on the ith load node at the kth time step; w is ai,hThe weight of the h load point on the ith load node is obtained;
Figure FDA0003133566280000013
the active load demand of the h load point on the ith load node is obtained; c. Ci,h,kThe cold load coefficient of the h load point on the ith load node at the kth time step; z is a radical ofi,h,kIs the recovery state of the h load point on the ith load node at the k time step, if z isi,h,k1, denotes the h-th load point recovery, if zi,h,k0; indicating that the h load point is not restored;
step 1.2, establishing direct current power flow constraint by using the formula (2) to the formula (7):
Figure FDA0003133566280000014
Figure FDA0003133566280000015
Figure FDA0003133566280000016
Figure FDA0003133566280000017
Figure FDA0003133566280000018
Figure FDA0003133566280000019
formula (2) to formula (7):
Figure FDA00031335662800000110
the maximum power angle difference of the power transmission line between the ith node and the jth node is represented; sij,kThe recovery state of the power transmission line between the ith node and the jth node at the kth time step is shown, if sij,k1, the power transmission line between the ith node and the jth node is recovered at the kth time step, if sij,kWhen the transmission line is not recovered, the transmission line between the ith node and the jth node is not recovered; deltai,kThe phase angle of the ith node in the kth time step; x is the number ofijRepresenting the reactance of the transmission line between the ith node and the jth node;
Figure FDA00031335662800000111
the active power transmitted on the transmission line between the ith node and the jth node at the kth time step;
Figure FDA00031335662800000112
the set of the transmission lines to be recovered at the kth time step;
Figure FDA00031335662800000113
the set of the recovered transmission lines at the k-1 time step;
Figure FDA00031335662800000114
the maximum active power which can be transmitted on the power transmission line between the ith node and the jth node is obtained;
Figure FDA00031335662800000115
active power output scheduled by the wind storage combined system on the ith node at the kth time step;
Figure FDA00031335662800000116
the active power output by the ith unit node at the kth time step; omegaLRepresenting a set of transmission lines;
Figure FDA00031335662800000117
the active load demand on the ith load node at the kth time step;
Figure FDA00031335662800000118
is the maximum phase angle at the ith node;
step 1.3, establishing a cold load constraint by using an equation (8) to an equation (14):
Figure FDA0003133566280000021
Figure FDA0003133566280000022
Figure FDA0003133566280000023
Figure FDA0003133566280000024
Figure FDA0003133566280000025
Figure FDA0003133566280000026
Figure FDA0003133566280000027
formula (8) -formula (14):
Figure FDA0003133566280000028
considering the active load demand after the cold load characteristic for the h load point on the ith load node at the kth time step;
Figure FDA0003133566280000029
the maximum active load after the cold load characteristic is considered for the h load point on the ith load node; lambda [ alpha ]i,h,αThe slope of a linear cold load characteristic curve of an h load point on an ith load node in an alpha section; zetai,h,α,kIs an auxiliary variable and represents the recovery time of the h load point on the i load node at the k time step in the interval
Figure FDA00031335662800000210
The length of time of the inner;
Figure FDA00031335662800000211
an alpha segment point of the linearized cooling load characteristic curve representing the h load point on the i load node;
Figure FDA00031335662800000212
an alpha-1 segment point of a linearized cooling load characteristic curve representing an h load point on an i load node;
Figure FDA00031335662800000213
representing the set of restored load points at time step k-1; t is ti,h,k-1The time that the h load point on the ith load node is recovered at the k-1 time step is represented; Δ tk,scRepresenting the load recovery duration of the load recovery upper-layer optimization model at the kth time step; n represents the number of segmentation points of the linearized cold load characteristic curve; v. ofi,h,α,kIs a Boolean variable and represents the kth time stepWhether the recovery duration of the h-th load point on the i load nodes is in the alpha section of the linearized cold load characteristic curve or not;
step 1.4, establishing unit output constraint by using the formula (15) to the formula (17):
Figure FDA00031335662800000214
Figure FDA00031335662800000215
Figure FDA00031335662800000216
formula (15) to formula (17):
Figure FDA00031335662800000217
representing the maximum active power allowed to be output by the g-th unit node at the k-th time step;
Figure FDA00031335662800000218
the active power output by the g unit node at the k-1 time step; r isgThe grade climbing rate of the g-th unit node is obtained;
Figure FDA00031335662800000219
the maximum active power allowed to be output for the g-th unit node; omegaGThe method comprises the steps of (1) collecting unit nodes;
Figure FDA00031335662800000220
representing the minimum active power allowed to be output by the g-th unit node at the k-th time step;
Figure FDA0003133566280000031
the minimum active power allowed to be output for the g-th unit node;
Figure FDA0003133566280000032
the active power actually output by the g-th unit node at the k-th time step;
step 1.5, establishing an optimal load input amount constraint by using an equation (18):
Figure FDA0003133566280000033
in formula (18):
Figure FDA0003133566280000034
the maximum load input allowed by the power system at the kth time step;
step 1.6, establishing unit standby constraint by using the formula (19) to the formula (20):
Figure FDA0003133566280000035
Figure FDA0003133566280000036
formula (19) -formula (20):
Figure FDA0003133566280000037
the reserve capacity of the g unit node at the k time step; rhogRepresenting the ratio of the reserve capacity of the g-th unit node in the total active output of the unit node;
step 1.7, establishing recovery state constraint by using the formula (21) to the formula (24):
Figure FDA0003133566280000038
Figure FDA0003133566280000039
Figure FDA00031335662800000310
Figure FDA00031335662800000311
formula (21) to formula (24): y isi,kIndicating the recovery state of the ith node at the kth time step if yi,k1, indicates that the ith node has recovered, if yi,k0, which means that the ith node is not recovered; ε is a constant;
Figure FDA00031335662800000312
the maximum load point number on the ith node is obtained;
step 1.8, establishing wind storage combined system dispatching output constraint by using a formula (25):
Figure FDA00031335662800000313
in formula (25):
Figure FDA00031335662800000314
the minimum active power output of the wind storage combined system accessed by the ith node at the kth time step;
Figure FDA00031335662800000315
the dispatching output of the wind storage combined system accessed by the ith node at the kth time step is obtained;
Figure FDA00031335662800000316
the maximum active power output of the wind storage combined system accessed by the ith node at the kth time step; omegaB,WThe method comprises the steps of collecting nodes of an accessed wind storage combined system;
step 1.9, the objective function shown in the formula (1) and the constraint conditions shown in the formulas (2) to (25) jointly form the load recovery upper-layer optimization model;
step two, establishing a load recovery lower-layer optimization model based on the alternating current power flow:
step 2.1, defining an objective function that minimizes the load recovery duration of the kth time step using equation (26):
minΔtk,xc (26)
in formula (26): Δ tk,xcLoad recovery duration for the load recovery underlying optimization model;
step 2.2, establishing an alternating current power flow constraint by using the formula (27) to the formula (28):
Figure FDA0003133566280000041
Figure FDA0003133566280000042
formula (27) to formula (28): u shapei,kThe voltage value of the ith node at the kth time step is shown;
Figure FDA0003133566280000043
restoring the power transmission line set restored by the upper-layer optimization model for the load at the kth time step; gijThe conductance value of the power transmission line between the ith node and the jth node is obtained; b isijThe susceptance value of the power transmission line between the ith node and the jth node is obtained;
Figure FDA0003133566280000044
the reactive power output of the ith unit node at the kth time step;
Figure FDA0003133566280000045
the reactive load demand on the ith load node at the kth time step;
and 2.3, jointly forming a load constraint considering the cold load characteristic in the load recovery lower-layer optimization model by using the formula (8), the formula (10) -the formula (13) and the formula (29) -the formula (31):
Figure FDA0003133566280000046
Figure FDA0003133566280000047
Figure FDA0003133566280000048
formula (29) -formula (31):
Figure FDA0003133566280000049
restoring the node set restored by the upper-layer optimization model for the load at the kth time step;
Figure FDA00031335662800000410
a set of load points on the ith load node;
step 2.4, establishing a unit output constraint by using the formula (32) -the formula (36):
Figure FDA00031335662800000411
Figure FDA00031335662800000412
Figure FDA00031335662800000413
Figure FDA00031335662800000414
Figure FDA00031335662800000415
formula (32) -formula (36):
Figure FDA00031335662800000416
representing the minimum reactive power allowed to be output by the g unit node;
Figure FDA00031335662800000417
the real output reactive power of the g-th unit node in the k-th time step;
Figure FDA00031335662800000418
representing the maximum reactive power allowed to be output by the g-th unit node;
step 2.5, establishing node voltage constraint by using the formula (37):
Figure FDA00031335662800000419
and 2.6, establishing a current step size correlation constraint by using an equation (38):
-Δtmin≤Δtk,xc-Δtk,sc≤Δtmin (38)
in formula (38): Δ tminThe minimum difference of the recovery duration between the load recovery upper-layer optimization model and the load recovery lower-layer optimization model is obtained;
step 2.7, the objective function shown in the formula (26) and the formula (8), the formula (10) -the formula (13), the formula (19), the formula (20), the formula (25) and the formula (27) -the formula (38) jointly form the load recovery lower layer optimization model;
step three, solving a load recovery double-layer optimization model considering the time-varying step length:
step 3.1, inputting initial data of the power system in the load recovery stage, wherein the initial data comprises the following steps: the output of the unit node, the load quantity of the recovered/unrecovered load point and the initial running state of the power system; and initializing k to 1;
step 3.2, solving a load recovery double-layer optimization model considering the step length of the time-varying step under the kth time step;
step 3.2.1, solving the load recovery upper layer optimization model by utilizing a solver CPLEX to obtain an optimal load recovery result at the kth time step, wherein the method comprises the following steps: the load point is recovered, and the transmission line is recovered;
step 3.2.2, transmitting the optimal load recovery scheme to the load recovery lower-layer optimization model, and solving the load recovery lower-layer optimization model by using a nonlinear solver SNOPT to obtain the shortest load recovery duration and the output of the optimal unit at the kth time step;
step 3.2.3, judging whether the load recovery double-layer optimization model at the kth time step meets the iteration termination condition, if so, executing the step 3.3, otherwise, after transmitting the optimal load recovery duration at the kth time step to the load recovery upper-layer optimization model, returning to the step 3.2.1; wherein the iteration termination condition is | Δ tk,sc-Δtk,xcDelta is less than or equal to | and the load recovery amount under the current time step is not changed any more;
step 3.3, outputting the optimal load recovery scheme of the kth time step, comprising: recovering the load point, the power transmission line, the duration and the output of the optimal unit;
and 3.4, judging whether all load points of the power system are recovered at the kth time step, if so, outputting an optimal load recovery scheme from the 1 st time step to the kth time step, otherwise, updating the running state of the power system, and returning to the step 3.2 after k +1 is assigned with k.
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